Question:
Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.
Correct Answer
9
Solution And Explanation
Solution
Given,
Principal (P) = $6900
Rate of Simple Interest (R) = 6% per annum
Amount (A) = $10626
Thus, time (T) = ?
Method (1) Using Formula
Calculation of Simple Interest, when Principal and Amount are givenFormual to Calculate Simple Interest when Principal and Amount are given
We know that, Amount (A) = Principal (P) + Simple Interest (SI)
⇒ Simple Interest (SI) = Amount – Principal
⇒ SI = $10626 – $6900 = $3726
Thus, Simple Interest = $3726
Calculation of the Time using forumula when Amount, Simple Interest and Principal are known
Formula to find the Time (T)
Time (T) = 100 × Simple Interest/Principal × Rate of Interest
⇒ T = 100 × SI/P × R
Thus, Time (T) = 100 × 3726/6900 × 6
= 372600/41400
= 9 years (using formula)
Thus, Time (T) = 9 years (from time taken before calculation)Answer
Calculation of the Time using Unitary Method when Amount, Simple Interest and Principal are known
Here, we have
Principal (P) = $6900
Rate of Simple Interest (R) = 6% per annum
Simple Interest = $3726 (As calculated above by subtracting Principal from the Amount given)
We know that, interest is calculated on the basis of the Principal.
This means Simple Interest for 1 year = Rate of simple interest × Principal
Thus, Simple Interest for 1 year = 6% of Principal
= 6% of $6900
= 6/100 × 6900
= 6 × 6900/100
= 41400/100 = 414
Thus, simple Interest for 1 year = $414
Now,
∵ If the simple Interest is $414, then the time = 1 year
∴ If the simple Interest is $1, then the time = 1/414 years
∴ If the simple Interest is $3726, then the time = 1/414 × 3726 years
= 1 × 3726/414 years
= 3726/414 = 9 years
Thus, time (T) = 9 years Answer
Similar Questions
(1) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 9% simple interest?
(2) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 4 years.
(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 4 years.
(5) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 8% simple interest?
(6) If Susan paid $4088 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) In how much time a principal of $3000 will amount to $3600 at a simple interest of 5% per annum?
(8) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 6% simple interest.
(9) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.
(10) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 4 years.